“…So motivation for the current studies arose from earlier results by the authors and the wish the research of polynomial of even degrees (6 th , 8 th and 10 th ) with maximum numbers of terms. An increase in number of the publications that deal with transition curves, both the railway and the road ones can indeed be observed (Ahmad and Ali, 2008;Ahmad et al , 2007;Droździel and Sowiński, 2006;Fischer, 2009;Habib and Sakai, 2003; Koc and Mieloszyk, 1987; Koc and Radomski, 1985;Kuvfer, 2000;Li et al , 2006;Long et al , 2010, Pombo andAmbrosio, 2003;Tanaka, 1935;Tari and Baykal, 2005;Woźnica, 2012;Zboiński, 2012;Zboiński, 2004). The same touches railway dynamics e.g.…”